Labour Supply on the Extensive Margin

Transcription

1 Labour Supply on the Extensive Margin The Participation Decision Miles Corak Department of Economics The Graduate Center, City University of New York Lecture 3 Labor Economics I ECON 87100

2 Introduction The labour force participation decision occurs at H = 0 for a labour force non-participant, that is to say, MRS XL > W /P at y the subjective rate of exchange of X and L exceeds the market rate of exchange the value of an additional hour of non-market time exceeds the value of commodities resulting from an additional hour of work. the labour force participant s utility maximization is an interior solution at H = 0 the MRS XL W /P implying that utility is higher when some time is spent working We define a binary variable that summarizes this P i = 0 iff H i = 0, that is MRS XL > W /P at H i = 0 P i = 1 iff H i > 0, that is MRS XL < W /P at H i = 0

3 Definition of the Reservation wage w R i MRS i XL(H i, w i, y i ) The reservation wage is the MRS XL subject to the full income budget constraint the location of the budget constraint and the utility function determine w R i

4 Definition of the Reservation wage w R i MRS i XL(H i, w i, y i ) The reservation wage is the MRS XL subject to the full income budget constraint the location of the budget constraint and the utility function determine wi R the value of of wi R at the endpoint of the budget constraint is the only value relevant for the participation decision wi 0 = MRSXL(H i i = 0, w i, y i ) Wi 0 = P wi 0 = P MRSXL(H i i = 0, w i, y i )

5 Definition of the Reservation wage w R i MRS i XL(H i, w i, y i ) The reservation wage is the MRS XL subject to the full income budget constraint the location of the budget constraint and the utility function determine wi R the value of of wi R at the endpoint of the budget constraint is the only value relevant for the participation decision wi 0 = MRSXL(H i i = 0, w i, y i ) Wi 0 = P wi 0 = P MRSXL(H i i = 0, w i, y i ) because of diminishing margin rates of substitution wi R are positive functions of H i W R i and

6 The market wage and the reservation wage The relationship between w and w R is the essence of the participation decision Consider an increase in the market wage the participation response to such a change depends upon the magnitudes of the change in w and the initial position of the individual

7 The market wage and the reservation wage The relationship between w and w R is the essence of the participation decision Consider an increase in the market wage the participation response to such a change depends upon the magnitudes of the change in w and the initial position of the individual if the individual is a labour force participant, the hours of work adjust but participation status is unchanged

8 The market wage and the reservation wage The relationship between w and w R is the essence of the participation decision Consider an increase in the market wage the participation response to such a change depends upon the magnitudes of the change in w and the initial position of the individual if the individual is a labour force participant, the hours of work adjust but participation status is unchanged if the individual is a labour force non-participant there are two possible responses

9 The market wage and the reservation wage The relationship between w and w R is the essence of the participation decision Consider an increase in the market wage the participation response to such a change depends upon the magnitudes of the change in w and the initial position of the individual if the individual is a labour force participant, the hours of work adjust but participation status is unchanged if the individual is a labour force non-participant there are two possible responses 1. no response

10 The market wage and the reservation wage The relationship between w and w R is the essence of the participation decision Consider an increase in the market wage the participation response to such a change depends upon the magnitudes of the change in w and the initial position of the individual if the individual is a labour force participant, the hours of work adjust but participation status is unchanged if the individual is a labour force non-participant there are two possible responses 1. no response 2. entry into the labour force

11 Ben-Porath (1973) develops a probabilistic framework helpful in predicting how the Labour Force Participation Rate (LFPR) changes for changes in parameters. It applies to groups of individuals, and two polar cases are examined, both of which predict δlfpr/δw > 0 Model A assumes preferences differ between individuals but the market wage is indentical Model B assumes the market wage differs between individuals but they all have identical preferences Focus on Model A in what follows, and leave the examination of Model B for individual work.

12 Model A: variable preferences, constant market wage rates A case in which tastes differ among individuals in the group (so that reservation wages differ), but market wage rates are identical for all members of the group. 1. Wi R = Wi R varies across group members, and is characterized by a probability distribution function g(w R ) 2. W i = W, market wage rates are the same for all members of the group Under these circumstances the group LFPR may be defined by assuming a particular form for the probability distribution function. participation occurs if W i > W R i. This inequality may be represented probabilistically as the area under the probability distribution function between 0 and W

13 Model A: variable preferences, fixed market wage rate Probability Distribution Function: Proposition 1 µ 1 Reservation Wage Distribution

14 Model A: variable preferences, fixed market wage rate Probability Distribution Function: Proposition 1 µ 1 Reservation Wage Distribution

15 Model A: variable preferences, fixed market wage rate Cummulative Distribution Function: Proposition 1 1 θ 1 0 µ 1 Reservation Wage Distribution

16 Model A: variable preferences, fixed market wage rate Cummulative Distribution Function: Proposition 1 1 θ 1 θ W 0 W µ 1 Reservation Wage Distribution

17 Model A: variable preferences, fixed market wage rate Probability Distribution Function: Proposition 1 A B W µ 1 Reservation Wage Distribution

18 Model A: variable preferences, fixed market wage rate Cummulative Distribution Function: Proposition 1 1 A+B A 0 W µ 1 Reservation Wage Distribution

19 Model A: variable preferences, fixed market wage rate θ g LFPR g = W 0 g(w )dw = G(W ) An immediate prediction is that LFPR g changes in the same direction as W θ 1 (W = W 1 ) = θ 2 (W = W 2 ) = W1 0 W2 0 g(w )dw = G(W 1 ) = A g(w )dw = G(W 2 ) = A + B The fact that A + B > A proves our proposition, another way of just saying G(W 2 ) > G(W 1 ) for W 2 > W 1, θ 2 > θ 1, implying δθ δw > 0

20 Aside on the statistical measurement of labour force concepts Labour force surveys, like the Current Population Survey in the United States, attempt to measure the faction of the population for which W R > W, the Labour Force Participation Rate. These are usually monthly surveys, and usually conducted during the week following the reference week, the week containing the 15th day of the month. Labour force survey concepts are measured according to respondent activity during the reference week

21 Aside on the statistical measurement of labour force concepts The determination of labour force status involves placing each individual in the survey into one of three categories: 1. Employed 2. Unemployed 3. Not in the labour force

22 Aside on the statistical measurement of labour force concepts Basic definitions 1. Employed (E)

23 Aside on the statistical measurement of labour force concepts Basic definitions 1. Employed (E) did any work at all at a job or business, that is, paid work in the context of an employer-employee relationship, or self-employment

24 Aside on the statistical measurement of labour force concepts Basic definitions 1. Employed (E) did any work at all at a job or business, that is, paid work in the context of an employer-employee relationship, or self-employment had a job but were not at work due to factors such as own illness or disability, personal or family responsibilities, vacation, labour dispute or other reasons

25 Aside on the statistical measurement of labour force concepts Basic definitions 1. Employed (E) did any work at all at a job or business, that is, paid work in the context of an employer-employee relationship, or self-employment had a job but were not at work due to factors such as own illness or disability, personal or family responsibilities, vacation, labour dispute or other reasons the Employment Rate is: ER = E/POP

26 Aside on the statistical measurement of labour force concepts Basic definitions 1. Employed (E)

27 Aside on the statistical measurement of labour force concepts Basic definitions 1. Employed (E) 2. Unemployed (U)

28 Aside on the statistical measurement of labour force concepts Basic definitions 1. Employed (E) 2. Unemployed (U) on temporary layoff during the reference week with an expectation of recall and were available for work

29 Aside on the statistical measurement of labour force concepts Basic definitions 1. Employed (E) 2. Unemployed (U) on temporary layoff during the reference week with an expectation of recall and were available for work or were without work, had looked for work in the past four weeks, and were available for work

30 Aside on the statistical measurement of labour force concepts Basic definitions 1. Employed (E) 2. Unemployed (U) on temporary layoff during the reference week with an expectation of recall and were available for work or were without work, had looked for work in the past four weeks, and were available for work or had a new job to start within four weeks from reference week, and were available for work

31 Aside on the statistical measurement of labour force concepts Basic definitions 1. Employed (E) 2. Unemployed (U) on temporary layoff during the reference week with an expectation of recall and were available for work or were without work, had looked for work in the past four weeks, and were available for work or had a new job to start within four weeks from reference week, and were available for work together E and U make up the Labour Force: LF = E + U

32 Aside on the statistical measurement of labour force concepts Basic definitions 1. Employed (E) 2. Unemployed (U) on temporary layoff during the reference week with an expectation of recall and were available for work or were without work, had looked for work in the past four weeks, and were available for work or had a new job to start within four weeks from reference week, and were available for work together E and U make up the Labour Force: LF = E + U the Unemployment Rate is: UR = U/LF

33 Aside on the statistical measurement of labour force concepts Basic definitions 1. Employed (E)

34 Aside on the statistical measurement of labour force concepts Basic definitions 1. Employed (E) 2. Unemployed (U)

35 Aside on the statistical measurement of labour force concepts Basic definitions 1. Employed (E) 2. Unemployed (U) 3. Not in the Labour Force (NILF)

36 Aside on the statistical measurement of labour force concepts Basic definitions 1. Employed (E) 2. Unemployed (U) 3. Not in the Labour Force (NILF) unwilling or unable to offer or supply labour services under conditions existing in their labour markets during the reference week

37 Aside on the statistical measurement of labour force concepts Basic definitions 1. Employed (E) 2. Unemployed (U) 3. Not in the Labour Force (NILF) unwilling or unable to offer or supply labour services under conditions existing in their labour markets during the reference week that is, they were neither employed nor unemployed

38 Aside on the statistical measurement of labour force concepts Basic definitions 1. Employed (E) 2. Unemployed (U) 3. Not in the Labour Force (NILF) unwilling or unable to offer or supply labour services under conditions existing in their labour markets during the reference week that is, they were neither employed nor unemployed the Labour Force Participation Rate (or just Participation Rate) is LFPR = LF /POP

39 Model A: variable preferences, fixed market wage rate Probability Distribution Function: Proposition 2 µ 1 Reservation Wage Distribution

40 Model A: variable preferences, fixed market wage rate Probability Distribution Function: Proposition 2 W µ 1 Reservation Wage Distribution

41 Model A: variable preferences, fixed market wage rate Probability Distribution Function: Proposition 2 W µ 1 µ 2 Reservation Wage Distribution

42 Model A: variable preferences, fixed market wage rate Two related propositions 1. An increase in the mean reservation wage implies that LFPR δθ falls, that is δµ < 0 W R 2. The closer the market wage is to the mode of the reservation wage distribution, the larger δθ δθ δw since δw = dg(w ) dw = g(w ) This latter prediction is consistent with the historical stylized facts, for example consider the substantial growth of the LFPR among women, who had participation rates around 50% a generation or so ago, implying W µ was the case.

43 Summary and things to do 1. Work through Model B in Ben-Porath (1973) 2. Use your understanding of labour supply on the intensive and extensive margin to complete the assignment, relying on course readings 3. Think about the presentation and term paper topics, and submit a ranked list of two to three topics you like to work on to the professor by before Tuesday, February 27 th.